Adaptive signal processing systems have many applications, including radar reception, cellular telephone and other communications systems, and biomedical imaging. Adaptive signal processing systems utilize adaptive filtering to differentiate between the desired signal and the combination of interference and noise, i.e., thermal or receiver noise. An adaptive filter is defined by four aspects: the type of signals being processed, the structure that defines how the output signal of the filter is computed from its input signal, the parameters within this structure that can be iteratively changed to alter the filter's input-output relationship, and the adaptive algorithm that describes how the parameters are adjusted from one time instant to the next.
Adaptive signal processing systems are required to filter out undesirable interference and noise. Due to the lack of a priori knowledge of an external interference environment, adaptive signal processing systems require a certain amount of statistically independent “weight training” data samples to effectively estimate the input noise and interference statistics.
Noise and interference may often hinder the desired signal detection. Noise is usually described as ever-present receiver thermal noise, generally at a lower power level. Interference may be intentional jamming or unintentionally received radiation. In these applications, antenna arrays, for instance, may change their multidimensional reception patterns automatically in response to the signal environment in a way that optimizes the ratio of signal power to the combination of interference power plus noise power (SINR). Adaptive arrays are especially useful to protect radar and communication systems from interference when the directions of the interference are unknown or changing while attempting to receive a desired signal of known form. Adaptive arrays are capable of operating even when the antenna elements have arbitrary patterns, polarizations, and spacings.
In many sensor system applications, adaptive signal processing is required to remove time-varying interference signals when attempting to detect weak, desired signals, or targets. In these dynamic signal environments, the interference characteristics change rapidly, and state-of-the-art “full rank” adaptive algorithms cannot adjust the weight vector (adaptive filter) fast enough. Methods exist called “reduced rank” adaptive processors that converge their weight vectors, in terms of SINR, faster than full rank methods, however these methods often have undesirable features, such as significant computational requirements, limitations on high-volume data throughput, wider main beams, sensitive parameter adjustments with required feedback, and other “side effects”. The rank generally refers to the number of interference or other noise sources for a given array system.
Adaptive processors such as Sample Matrix Inversion (SMI), or the numerically equivalent Gram-Schmidt Cascaded Canceller (GSCC), utilize multi-channel, or multi-sensor, measured input data to estimate the signal environment in order to mitigate interference and noise while preserving target energy. The ability to adapt is often required because adequate a priori knowledge of the interference and noise statistics is not available. For radar applications, for example, the interference and noise environment consists of jamming, ground clutter, and receiver noise. To form weights used in a linear adaptive processor, the interference plus noise covariance matrix often is estimated, either directly or indirectly, using measured training data from the input channels. These SMI methods are known to be equivalent to procedures that minimize least squares cost functions of the input training data to produce the adaptive weight vector. Least squares methods are well known to exhibit non-robust behavior. SMI methods are known to be optimal in several respects when the input data vectors are independent and identically distributed (i.i.d.) and Gaussian.
The SINR convergence measure of effectiveness (MOE) is the number of stationary, independent and identically distributed (i.i.d.) data samples per input sensor (i.e., snapshots), the number of weight training data, that are required so that the average SINR of the adaptive processor is nominally within 3 dB of optimum (i.e., optimum is 0 dB). It is desired to minimize the SINR convergence MOE to accommodate non-stationary data that is due to, for example, non-homogenous clutter, multiple targets, outliers, and/or a volatile jamming environment. In addition, faster convergence may reduce computations and cost. The convergence MOE of SMI or any numerically equivalent implementation of SMI, such as the GSCC, can be attained using approximately 2N i.i.d. snapshots for weight estimation in pure stationary Gaussian interference noise environments. The integer N denotes the number of degrees of freedom (DOF), or the number of input channels, or sensors, to the adaptive processor. For example, N is the number of antenna channels (i.e., antenna elements or subarrays) for a spatially adaptive array processor, and is the number of space and time channels for Space-Time Adaptive Processing (STAP) processor. SMI's 2N convergence MOE is known to be independent of any external interference covariance matrix, i.e., independent of the effective rank of the input covariance matrix, when the i.i.d. and Gaussian assumptions are strictly satisfied. Effective rank denotes the number of eigenvalues of the input sample covariance matrix that are large compared to the remaining, ideally equal, and small, eigenvalues that are usually associated with the received noise levels. This independence feature is very useful in practice since it provides the designers of adaptive radar systems with an a priori, fixed value for the number of required training snapshots (in ideal Gaussian environments) for a given system's DOF.
Reduced rank processors are a class of algorithms that converge more quickly than full rank processors. A full rank processor's convergence MOE (i.e., SMI or GSCC) often is proportional to (e.g., twice) the number of input channels, N, or degrees of freedom (DOF) (e.g. DOF=10 to 1000). A reduced rank processor's convergence MOE is generally proportional to (e.g., twice) the effective rank, R, of the input interference covariance matrix, which may be much smaller than the DOF in many interference environments (e.g., effective rank=1 to 100).
Reduced rank refers to methods whereby, in some cases, the adaptive processor converges in SINR using fewer subspace directions than full rank, where full rank corresponds to the dimension of the input data or the adaptive DOF often denoted as the variable N. In all cases, optimal, desired convergence occurs in near 2N training samples for full rank processors and less than 2N for reduced rank processors.
A soft weighting processing technique is desired that can be reiteratively applied to adaptive signal processor algorithms to produce adaptive convergence rates that are as fast or faster than full rank processing algorithms. One such exemplary full rank algorithm has been described in U.S. Pat. No. 6,904,444 Picciolo, Gerlach, and Goldstein, entitled “PSUEDO-MEDIAN CASCADED CANCELLER.” Another such algorithm is the Gram-Schmidt Cascaded Canceller, and any other generic cascaded canceller algorithm, whether in full or reduced rank form, may also be implemented to make use of the invention. Examples of generic cascaded cancellers are referenced and may be found in Picciolo, M. L., Schoenig, G. N., Mili, L., Gerlach, K., “Rank-Independent Convergence For Generic Robust Adaptive Cascaded Cancellers Via Reiterative Processing”, Proceedings of IEEE International Radar Conference, Washington, D.C., May 9-12, 2005, pp. 399-404, and Picciolo, M., “Robust Adaptive Signal Processors”, PhD Dissertation, Virginia Tech, Apr. 18, 2003. Such a processing technique may also be applied to reduced rank algorithms, such as multi-stage median cascaded canceller, which has been described in U.S. Pat. No. 7,167,884 to Picciolo, Gerlach, and Goldstein, entitled “MULTI-STAGE MEDIAN CASCADED CANCELLER,” to further improve convergence. Another exemplary algorithm is a Multi-Stage Weiner Filer (MWF), which may be implemented with Gram-Schmidt weighting in its synthesis stage.
It is desired to have an algorithm that performs superior to full rank and reduced rank processors in practice when ideal assumptions for the input training data are violated. One such reduced rank processor that performs poorly with non-ideal training data is the FML (Fast Maximum Likelihood), which involves forming the eigenvalues/eigenvectors of the sample covariance matrix of the input data, and selecting those eigenvalues at or below the thermal noise level to be replaced by the noise power level value, and then forming an inverse matrix with the set of all eigenvectors and the set of (partially modified) eigenvalues as described by M. Steiner, and K. Gerlach, “Fast Converging Adaptive Processor For A Structured Covariance Matrix”, IEEE Trans. Aerospace and Elect. Syst., Vol. 36, No. 4, October 2000, pp. 1115-1126. Another such processor is the PCI (Principal Components' Inverse), which involves forming the eigenvalues/eigenvectors of the sample covariance matrix of the input data, and selecting those eigenvectors associated with the largest eigenvalues, and forming an inverse matrix with that subset of eigenvectors and associated eigenvalues as described by J. R. Guerci and J. S. Bergin in “Principal Components, Covariance Matrix Tapers, and the Subspace Leakage Problem”, IEEE Trans. Aerospace and Electronic Systems, Vol. 38 No. 1, January 2002, pp. 152-162.
It is further desired to have an algorithm that is simple, computationally fast, and significantly improves the convergence rate of full and reduced rank processors such as cascaded cancellers and MWFs in terms of important metrics such as SINR, Probability of Detection (Pd), and Bit Error Rate (BER). It is desired to achieve flexibility for adaptive processing applications that require fast convergence (due to low sample support and/or computational restrictions), low adaptive sidelobes, and high adaptive filter resolution (i.e., high number in input channels or degrees of freedom).